The invention relates to the field of imaging in a scattering medium, and in particular to a method of minimizing inter-parameter crosstalk in imaging the internal properties of a scattering medium.
Imaging of a scattering medium relates generally to an imaging modality for generating an image of the spatial distribution of properties (such as the absorption or scattering coefficients) inside a scattering medium through the introduction of energy into the medium and the detection of the scattered energy emerging from the medium. These systems and methods are in contrast to projection imaging systems, such as x-ray. X-ray systems, for example, measure and image the attenuation or absorption of energy traveling a straight line path between the x-ray energy source and a detector, and not scattered energy. Whether the energy is primarily highly scattered or primarily travels a straight line path is a function of the wavelength of the energy and medium it is traveling through.
Imaging based on scattering techniques permits the use of new energy wavelengths for imaging features of the human body, earth strata, atmosphere and the like that were unable to be imaged using projection techniques and wavelengths. For example, x-ray projection techniques may be adept at imaging bone structure and other dense objects, but are relatively ineffective at distinguishing and imaging blood oxygenation levels. This is because the absorption coefficient of blood does not vary significantly with blood oxygenation, at x-ray wavelengths. However, infrared energy can identify the spatial variations in blood volume and blood oxygenation levels because the absorption coefficient at this wavelength is a function of hemoglobin states. Other structures and functions can be identified by variations or changes in the scattering coefficient of tissue exposed to infrared energy, such as muscle tissue during contraction, and nerves during activation. These structures could not be imaged by projection techniques because projection techniques are not effective in measuring variations in scattering coefficients. These measures, obtainable through imaging based on scattering techniques, such as optical tomography, have considerable potential value in diagnosing a broad range of disease processes.
A typical system for imaging based on scattered energy measures, includes at least one energy source for illuminating the medium and at least one detector for detecting emerging energy. The energy source is selected so that it is highly scattering in the medium to be imaged. The source directs the energy into the target scattering medium and the detectors on the surface of the medium measure the scattered energy as it exits. Based on these measurements, a reconstructed image of the internal properties of the medium is generated.
The reconstruction is typically carried out using xe2x80x9cperturbation methodsxe2x80x9d. These methods essentially compare the measurements obtained from the target scattering medium to a known reference scattering medium. The reference medium may be a physical or fictitious medium which is selected so that it has properties that are as close as possible to those of the medium to be imaged. Selecting a reference medium is essentially an initial guess of the properties of the target. In the first step of reconstruction, a xe2x80x9cforward modelxe2x80x9d is used to predict what the detector readings would be for a particular source location based on the known internal properties of the reference medium. The forward model is based on the transport equation or its approximation, the diffusion equation, which describes the propagation of photons through a scattering medium. Next, a perturbation formulation of the transport equation is used to relate (1) the difference between the measured and predicted detector readings in the target and reference, respectively, to (2) a difference between the unknown and known internal properties of the target and reference, respectively. This relationship is solved for the unknown scattering and absorption properties of the target. The final distributions of internal properties are then displayed or printed as an image.
Imaging systems based on scattering techniques, such as optical tomography systems, provide a means with which to examine and image the internal properties of scattering media, such as the absorption and diffusion or scattering coefficients. However, a problem with the known systems and methods-is that of inter-coefficient crosstalk. Inter-coefficient or parameter crosstalk refers to instances where, for example, localized variations in absorption appear, in the recovered image, as localized variations in scattering, or vice versa. For instance, the vasculature can be imaged because the absorption coefficient of the blood contrasts with the absorption coefficient of the surrounding tissue. Similar variations in the scattering or diffusion coefficient may be present through the tissue as a result of glucose levels or nerve activation. The problem of crosstalk relates to determining whether a change in a detector reading on the surface of the target is the result of a change in the absorption coefficient or the scattering coefficient. The problem is that in the attempt to image the vasculature by examining absorption coefficients, the image may be distorted by variations in the scattering or diffusion coefficient that have leaked into the absorption coefficient.
For the foregoing reasons, there is a need for a method of minimizing inter-coefficient crosstalk to more accurately and reliably resolve the scattering and absorption coefficients in image reconstruction.
The present invention satisfies this need by providing a method and system for image reconstruction and data collection that minimizes inter-coefficient crosstalk.
One object of the invention is to minimize crosstalk by (1) generating a system of linear perturbation equations, (2) scaling the weight matrix or matricies of the linear perturbation equations, and (3) constraining the solution of the linear equations by either (a) applying one of a positive or a negative constraint where the direction of the perturbation is known, or (b) solving the system of linear perturbation equations twice, first with a positivity constraint and second with a negativity constraint where the direction of the perturbation is unknown. The linear perturbation equations solved with a positivity constraint are only permitted to have a positive perturbation in the solution at each iteration, any negative solutions are overridden; a negative constraint only permits negative solutions. The positively and negatively constrained solutions may then be summed to produce a solution with minimal crosstalk.
A further aspect of the invention is to minimize crosstalk by using relative detector values in place of absolute values in the linear perturbation equations.
Using the inventive techniques, the crosstalk between the internal properties such as the absorption and scattering coefficient can be minimized and the coefficients more clearly resolved so that perturbations in one coefficient do not effect the other.
The foregoing specific objects and advantages of the invention are illustrative of those which can be achieved by the present invention and are not intended to be exhaustive or limiting of the possible advantages that can be realized. Thus, the objects and advantages of this invention will be apparent from the description herein or can be learned from practicing the invention, both as embodied herein or as modified in view of any variations which may be apparent to those skilled in the art. Accordingly, the present invention resides in the novel parts, constructions, arrangements, combinations and improvements herein shown and described.